Barycentric measure of quantum entanglement

TL;DR

This paper introduces a barycentric measure of quantum entanglement based on the Majorana representation, analyzing how the distribution of points on the sphere reflects the state's coherence or entanglement, and explores their dynamics under unitary evolution.

Contribution

It proposes a novel entanglement measure derived from the variance of Majorana point distributions and studies their behavior under quantum dynamics.

Findings

Variance of Majorana point distribution correlates with entanglement levels.

Majorana point dynamics reflect quantum state evolution.

The measure distinguishes between coherence and entanglement.

Abstract

Majorana representation of quantum states by a constellation of n 'stars' (points on the sphere) can be used to describe any pure state of a simple system of dimension n+1 or a permutation symmetric pure state of a composite system consisting of n qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of non-coherence for simple systems, or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of the pure state is investigated.